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JAMB Mathematics 2016 Paper

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Question : 33

Total: 50

If y = 2x³ + 6x² + 6x + 1, Find

\frac{dy}{dx}

6x² + 12x + 1
6x² + 6x + 1
6x² + 6x + 6
6x² + 12x + 6

Solution:

Concept:

Differentiation of a polynomial using the power rule.

Explanation:

Given

y = 2x^3 + 6x^2 + 6x + 1

.

Differentiate each term with respect to

x

.

For

2x^3

, the derivative is

6x^2

.

For

6x^2

, the derivative is

12x

.

For

6x

, the derivative is

6

.

For the constant

1

, the derivative is

0

.

Thus

\frac{dy}{dx} = 6x^2 + 12x + 6

.

Answer:

\frac{dy}{dx} = 6x^2 + 12x + 6

Correct option: D.

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